Oct 4 Automorphism of complex surfaces:
What is the simplest interesting dynamical system?
Oct 18. Curves in the space of quadratic rational maps
Nov 1. The 3D dimer model
Nov ?. Multipliers of rational maps
Dec 6. Stretch maps, after Thurston
Feb 8. Galois orbits, equidistribution, and the moduli space of all triangles
Feb 15. Entropy and geodesic currents on surfaces
Feb 22. Earthquakes, triangulations and circle homeomorphisms
Sep. 7, 14: Exotic homeomorphisms and flows (after Sullivan and Freedman)
Sep. 21, 28, Oct 5, 12, 19: Billiards and Teichmuller theory
Oct 26: Unramified correspondences (Bogomolov, Tschinkel)
Nov 2: A norm for the homology of 3-manifolds (Thurston)
Nov 9, 16: Bers, Hénon, Painlevé and Schrödinger (Cantat)
Nov 30: Triangles groups and Hilbert modular varieties.
Sep. 11: Absolute periods of holomorphic 1-forms on Riemann surfaces
Sep. 18: On the Loewner energy of simple planar curves
Oct. 2: Elementary surfaces in the Apollonian manifold
Oct. 9: From veering triangulations to pseudo-Anosov flows (and back again)
Oct. 23: The Weil-Petersson gradient flow for renormalized volume
Oct. 30: A walk from knots to exotic smooth Stein 4-manifolds
Nov. 6: Level sets of length function in moduli space
Nov. 13: Experimental study of a meromorphic analogue of Teichmüller space
Nov. 20: Volumes and intersection theory on moduli spaces of differentials
Andreev's theorem on hyperbolic polyhedra and Kleinian reflection groups
18 April: Galois conjugates of PCF generalized beta-transformations
11 April: Kaehler groups and surface bundles
4 April: What to do when you cannot confine your planes? Teichmüller spaces of non-compact Riemann surfaces
28 March: Planes immersed in hyperbolic 3-manifolds
21 March: Bounds on renormalized volume and the volume of the convex core
7 March: The geometry of Hilbert's 13th problem
*7 March: The theory of resolvent degree, after Hamilton, Klein, Hilbert, and Brauer
28 Feb: 5 points on the sphere
21 Feb: Convex cores of thick hyperbolic 3-manifolds with bounded rank
14 Feb: Hypergeometric equations and Lyapunov exponents (via Hodge theory)
7 Feb: Penrose Tilings of Riemann Surfaces
31 Jan: The behavior of planes in confinement
29 Nov: Finitely many algebraically primitive Teichmüller curves in genus g at least 3
8 Nov: Square-tilings of modular curves X(d)
1 Nov: Cohomology of arithmetic groups and characteristic classes of manifold bundles
25 Oct: The metastable homology of mapping class groups
18 Oct: Algebraic dynamics from topological and holomorphic dynamics
4 Oct: Divergent trajectories in arithmetic homogeneous spaces of rational rank two
27 Sep: Trees in degenerating families of rational maps and isometric G-actions
20 Sep: Plane curves, (higher) spin structures, and mapping class groups
13 Sep: Tilings and Hurwitz theory
Feb 2: The number of non-negative curvature triangulations of the sphere
Feb 8: Flat surfaces and stability structures on categories
Feb 15: Constructing pseudo-Anosov mapping classes with small stretch factor
Feb 22: Strata of abelian differentials and the effective cone of M_g,n
March 1: Global dynamics of multicurves in complex dynamics
March 8: Extremal and rigid divisors on moduli spaces of curves
March 22: Differentiating Blaschke products
March 29: Smooth compactifications of strata of abelian differentials
April 5: Berkovich spaces and complex dynamics
April 12: Rationality of canonical height
April 19: Affine surfaces part I
April 25: Affine surfaces part II
Sep 14, 21: Almost simple geodesics on the triply-punctured sphere |
Feb 4: Kronecker's congruence and Teichmüller curves in
Feb 11: Transversality
Feb 18: Rubber Bands and Rational Maps
Feb 25: Equidistribution of Shears and Applications
March 4: Circle actions on the boundary of Schottky space
March 11: Hyperbolic extensions of free groups
March 18: Have a good Spring Break!
March 25: Generalizing Douady's Magic Formula
April 1: On the classification of critically fixed rational maps
April 15: Families of K3 surfaces and their asymptotic properties
April 22: A case of the dynamical André-Oort conjecture
April 29: A polynomial endomorphism of C^2 with a wandering Fatou component
May 1-3: Reading Group Reunion, Harvard University
May 13: Complex dynamics and elliptic curves
Normalized entropy versus volume (Kojima-McShane)
The renormalized volume and the volume of the convex core of quasifuchsian manifolds (Schlenker)
Geometric inflexibility and 3-manifolds that fiber over the circle (Brock-Bromberg)
Zippers and univalent functions (Thurston)
The Schlaefli formula in Einstein manifolds with boundary (Rivin and Schlenker)
The hyperbolic Gauss map and quasiconformal reflections (Epstein)
NotesLecture 1 (McMullen)
Lecture 2 (Bridgeman)
Lecture 3 (Yarmola)
Lecture 4 (Bridgeman)
Lecture 5 (Brock)
Lecture 6 (McMullen)
R. Mukamel, Stanford University
G. Tiozzo, Harvard University
H. Masur, University of Chicago
H. Shiga, Tokyo Institute of Technology
A. Karlsson, University of Geneva
K. Pilgrim, Indiana University
J. Smillie, Cornell University
L. DeMarco, University of Illinois at Chicago
A. Sambarino, Orsay
M. Bainbridge, Indiana University
S. Antonakoudis, Harvard University
Y. Ishii, Kyushu University
J. H. Hubbard, Université de Provence/Cornell University
B. Farb, University of Chicago
O. Ivrii. Ghosts of the mapping class group. 11 Jan.
G. Tiozzo. Entropy and dimension of sets of external rays. 11 Jan.
C. McMullen. Navigating moduli space with complex twists. 11 Jan.
2/29: Matings with laminations
Dzmitry Dudko, Jacobs University
X. Buff. Antipode-preserving cubic rational maps. 6 June
10/12: A proof of Pilgrim's conjecture
Nikita Selinger, SUNY Stony Brook
C. McMullen. Periodic, Diophantine and ergodic foliations on surfaces. 9 Feb - 9 Mar.
J. Hubbard. On the density of Strebel differentials. 23 March.
S. Koch. On the Deligne-Mumford compactification of moduli space. 6, 13 April.
N. Dunfield. The least spanning area of a knot and the Optimal Bounding Chain Problem. 20 April.
M. Duchin. Flat structures as currents. 27 April.
C. McMullen. Manifolds, topology and dynamics: Milnor's work and subsequent developments. 11 May.
C. McMullen. What is a K3 surface? 27-30 June.
R. Kirby. A new calculus for 4-manifolds. 8 Sep. |
L. DeMarco. Dynamics of cubic polynomials and enumeration of cusps. 15 Sep.
C. McMullen The evolution of geometric structures on 3-manifolds. 20 Sep. (Monday)
T. Koberda. A ping-pong theorem for the mapping-class group. 29 Sep.
V. Gadre. Singularity of harmonic measures for random walks on the mapping class group. 6 Oct.
J. Bourgain. Expansion in linear groups (4:30, Lecture Hall D). 13 Oct.
R. Roeder. Blaschke products and renormalization on the diamond hierarchical lattice. 20 Oct.
X. Buff. Transversality for Herman rings. 27 Oct.
E. Uhre. The Mandelbrot set and its deformations. 3 Nov.
G. Tiozzo. Continued fractions and kneading sequences of unimodal maps. 17 Nov.
D. Meyer. Invariant Peano curves of expanding Thurston maps. 1 Dec.
C. McMullen. Entropy. 10, 17 Feb. |
M. Baker. Complex dynamics and adelic potential theory. 24 Feb
C. McMullen. Surface dynamics. 3, 10 March
T. Koberda. Surface bundles of small volume. 24 March
G. Tiozzo. Absolute continuity of invariant measures for random walks on Lie groups. 31 March
R. Mukamel. Teichmueller dynamics in genus two, modular forms and zeta functions. 7 April
S. Koch. Dynamics in superattracting basins. 14 April
A. Putnam. The Picard group of the moduli space of curves with level structures. 21 April
D. Margalit. Symplectic representations of braid groups. 28 April
G. Walsh. The bumping set and the characteristic submanifold. 5 May
E. Hironaka. Small dilatation pseudo-Anosov mapping classes coming from the simplest pseudo-Anosov braid.
H. Oh. Equidistribution and counting for geometrically finite hyperbolic groups.
S. Fenley. Pseudo-Anosov flows and large scale geometry of 3-manifolds.
S. Koch. Dynamics of maps on moduli space.
M. Bridgeman. The orthospectra of finite volume hyperbolic manifolds with totally geodesic boundary and associated volume identities.
A. Cotton-Clay. Holomorphic Pants in R times a mapping torus.
D. Margalit. Small dilatation pseudo-Anosovs and 3-manifold.
G. Walsh. Commensurability of knot complements.
G. Tiozzo. The entropy of alpha-continued fractions
Apollonian circle packings and horosphercial flows on hyperbolic
Wed, 18 Feb
D. Margalit. Torelli groups and the complex of minimizing cycles. Wed, 25 Feb
R. Devaney. Dynamics of zn + C/zn: Why n=2 is crazy. Wed, 4 March
E. Hironaka. Pseudo-Anosov mapping classes with small dilatation constructed from graphs. Wed, 11 March
A. Wilkinson. Absolute continuity, Lyapunov exponents and rigidity. Wed, 18 March
D. Damjanovic. Perturbations of some higher rank unipotent actions Wed, 1 Apr
N. Shah. Limits of expanding translates of shrinking curves on hyperbolic manifolds. Wed, 8 April
C. Taubes. An introduction to geometric quantization. Wed, 15 Apr
A. Bufetov. Suspension flows over Vershik's automorphisms. Wed, 22 Apr
E. Ghys. Dynamics in Dimension 3. (Talk at MIT: room 34-101, 4:30 pm.) Wed, 29 Apr
T. Koberda. Braids and Their Dilatations: The Burau, Gassner and Bigelow representations. Wed, 3 May
Random walks on the hyperbolic plane and barycenter subdivision.
Wed, 15 Oct |
C. McMullen. Braid groups and Hodge theory. Wed, 22 Oct
R. Schwartz. Outer billiards and the modular group. Wed, 29 Oct
D. Fisher. The space of discrete linear groups. Wed, 5 Nov
J. Duncan. Fuchsian groups and affine Dynkin diagrams. Wed, 12 Nov
N. Avni. Dynamics on representation varieties --- finite, compact and hyperbolic. Wed, 19 Nov
S. Sheffield Hamburgers, cheeseburgers, and scaling limits of discrete random surfaces. Wed, 3 Dec
R. Mukamel Surfaces with triangular veech broups Wed, 10 Dec
Hyperbolic surfaces and systems of arcs.
Wed, 14 March |
D. Kleinbok. Expanding translates of horospheres and applications to number theory. Wed, 21 March
J. Behrstock. Asymptotic geometry of the mapping-class group. Wed, 4 April
L. Silberman. Measure rigidity for Cartan actions: the "low-entropy" method. Wed, 11 April
D. Damjanovic. Littlewood's conjecture and SL_3(R)/SL_3(Z). Wed, 25 April
S. Brooks. Halfway to quantum unique ergodicity. Wed, 2 May
C. McMullen. Complex dynamics on the unit disk: measures, multipliers and R-trees. Wed, 9 May
D. Dumas. Grafting and shearing hyperbolic surfaces |
M. Bainbridge. Volumes of Hilbert modular surfaces
M. Mirzakhani. Ergodic properties of the space of measured laminations
C. McMullen. Thermodynamics, dimension and the Weil-Petersson metric
R. Schwartz. Nearly isosceles billiards, Veech points, and universal power series expansions
J. Brock. Heegaard splittings, handlebodies and the geometry of hyperbolic 3-manifolds
Mon, May 9. Prym varieties and Teichmüller space.
Curt McMullen |
Wed, May 11. Euler characteristics of Teichmüller curves. Matt Bainbridge
Mon, May 16. Coble sextics and holomorphic actions of lattices on P1. Izzet Coskun
Wed, May 18. Polynomial dynamics and trees. Laura DeMarco
Wed, May 25. Hausdorff dimension and bendings of Fuchsian groups. Martin Bridgeman
Fri, May 27. Train tracks. Maryam Mirzakhani
Oct. 22. Markov maps and discreteness tests for punctures torus
groups. David Dumas
Oct. 29. The boundary of the space of rational maps. Laura DeMarco.
Nov. 5. Is there a polynomial Julia set of positive measure? Matt Bainbridge.
Nov. 20. Crystals and algebraic curves. Colloquium, Andrei Okounkov (Princeton)
Dec. 12. Billiards and dynamics over moduli space. Gauge theory seminar, Curt McMullen
Sept. 25. Billiards and Riemann surfaces of infinite complexity. Curt McMullen.
Oct. 2. Galois flux and measured foliations. Curt McMullen.
Oct. 9. What is a random 3-manifold and what does it look like? Nathan Dunfield.
Oct. 16. Does a random 3-manifold fiber over the circle? Nathan Dunfield.
Oct. 23. No meeting. Go to Rich Schwartz's colloquium on Thursday instead.
Oct. 30. Physical measures and periodic orbits of quadratic polynomials. Matt Bainbridge.
Nov. 6. Moduli of Polyhedra. Laura DeMarco.
Nov. 13. Ergodic theory of horocycles and the earthquake flow on moduli space. Maryam Mirzakhani.
Nov. 20. Is the Jones polynomial the same size as the Alexander polynomial? Jacob Rasmussen.
Nov. 27. No meeting
Dec. 4. Abelian differentials and dynamics Izzet Coskun.
Dec. 11. Projective Riemann surfaces with Fuchsian holonomy David Dumas.
Dec. 18. The Patterson-Sullivan theory of discrete quasiconformal groups Ed Taylor.
Jan 30. Billiards and Curves of Genus 2. Curt McMullen.
Feb 6. Laminations and groups of homeomorphisms of the circle. Nathan Dunfield.
Feb 13. The configuration space of points on the projective line and the moduli of polygons. Haruko Nishi.
Feb 20. Simple geodesics and the Weil-Petersson volume of the moduli space of Riemann surfaces. Maryam Mirzakhani.
Feb 27. Experiments with Quasifuchsian Groups and Projective Structures. David Dumas.
Mar 6 (starts 4:30). Growth of the number of periodic points for generic diffeomorphisms. Vadim Kaloshin.
Mar 13. Some algebraic questions related to the Poincaré Conjecture. Andrew Casson.
Mar 20. A Variational Study of Curvature and Potential Theory. Laura DeMarco.
Mar 27. Spring Break.
Apr 3. Complex hyperbolic reflection groups: a primer. Daniel Allcock.
Apr 10. Rigidity and non-rigidity of hyperbolic 3-manifolds. Kevin Scannell.
Apr 17. Shadow pictures: pair-of-pants decompositions of 3-manifolds. Dylan Thurston.
Apr 24. Weil-Petersson and Hodge volumes of moduli space, and the Schottky problem. Samuel Grushevsky.
May 1. Mostow Rigidity and Lattice Classification. Kathy Paur.
2. The boundary of an abstract group and simple loops on the torus, C. McMullen
3. Surfaces in finite covers of 3-manifolds: the virtual Haken conjecture, N. Dunfield
4. Circles and hyperbolic geometry I, D. Calegari
|Euler class of E| <= |Euler class of TS|.
5. Circles and hyperbolic geometry II, D. Calegari
6. Hyperbolic volume and the Jones polynomial, D. Thurston
7. Lyapunov exponents and complex dynamics, L. DeMarco
8. Julia sets, harmonic measure and rotation, I. Binder
9. The topology of the space of hyperbolic structures on a 3-manifold, J. Holt
10. Complex projective structures on Riemann surfaces, D. Dumas
11. Simple closed curves on surfaces and the volume of moduli space, M. Mirzakhani
12. Dynamics on K3 surfaces, C. McMullen
13. Exotic complex projective surfaces and the boundaries of quasifuchsian and Schottky spaces, H. Tanigawa
2. Cusps of hyperbolic manifolds and the boundary of the Mandelbrot set, C. McMullen
3. 3-manifold groups, surfaces and actions on trees, N. Dunfield.
4. Surgery on 3-manifolds and volume rigidity, N. Dunfield.
5. Teichmüller space, quadratic differentials and rational billards, H. Masur.
6. Counting periodic points for billiards and flat structures, H. Masur.
7. Salem numbers in geometry, Eriko Hironaka
8. Average bending of convex hull boundaries, M. Bridgeman
9. Currents and instability in complex dynamics, Laura DeMarco
10. Foliated Teichmüller theory, C. McMullen
11. Diophantine numbers, quadratic differentials and failure of ergodicity, Yitwah Cheung
12. An Approach to the Low-Volume Question for Hyperbolic 3-Manifolds, Robert Meyerhoff
2. Lipschitz maps and nets in Euclidean space
3. Periods; dynamics
4. The Mandelbrot set is connected
5. Schottky groups and Teichmüller space
6. Earthquakes and hyperbolic geometry
7. Complex dynamics, measures and foliations
8. Compactness in moduli space
9. Simple closed curves
10. Geodesic currents
11. The Nielsen problem
12. Teichmüller space is a domain of holomorphy
13. Extremal length, univalent maps and Teichmüller space